Question

If the volumes of two cones be in the ratio 1:4 and the radii of their bases be in the ratio 4:5 then the ratio of their heights is​

Answer 1

Answer:

25/64

Step-by-step explanation:

Answer 2

The ratio of their heights is​ 25:64.

Given, the radius of the bases of the cones are in the ratio 4:5

Let us consider the radius of them to be 4x and 5x.

We know,

Volume of a cone is given as (1/3)Пr²h

h is the height of the cone

For, the cone with radius 4x and height h, volume V = (1/3)П(4x)²h = 16Пx²h/3

For, the cone with radius 5x and height h', volume V' = (1/3)П(5x)²h' = 25Пx²h'/3

Given, V/V' = 1/4

⇒[16Пx²h/3]/[25Пx²h'/3] = 1/4

⇒ 16h/25h' = 1/4

⇒ h/h' = 25/64

This is the ratio of their heights.